Blood Alcohol Concentration (Widmark) Calculator
Blood Alcohol Concentration (Widmark) Calculator
Estimate a blood alcohol concentration from drinks using the Widmark equation — and see the published range around that estimate, which on this page’s own default inputs is wide enough to straddle two legal limits at once. This cannot tell anyone whether they are fit or legal to drive.
Widmark BAC estimate
Drinks → BAC, with its rangeAn 80 kg man, three 568 mL drinks at 4.5% ABV, three hours since the first drink, β 0.015 g/100 mL/h
The equation, both ways round, and where 0.82 comes from
Rearranged for the concentration: Ct = d · Z · N ÷ (W · r) − β t
As this page computes it, in metric:
A (g ethanol) = drink volume (mL) × ABV ÷ 100 × 0.789
BAC (g/100 mL) = A ÷ (10 · r · Wkg) − β · t
- N, W, Z, d
- the published form solves for N, the number of drinks, from a known concentration — which is what a forensic expert is usually asked to do. W is body weight in ounces, Z is fluid ounces of ethanol per drink, d is the density of ethanol in oz/fl oz
- d = 0.82
- not a fudge factor and not 0.8. Ethanol’s density is 0.789 g/mL, and 0.789 × 29.5735 mL/fl oz ÷ 28.3495 g/oz = 0.8231 oz/fl oz — so Gullberg’s 0.82 is ethanol’s density written in the units his equation uses. Working in metric, as this page does, removes the constant entirely and leaves the 0.789 g/mL
- r
- the volume of distribution in L/kg, Widmark’s 0.68 for men and 0.55 for women. It is a body-composition term: ethanol distributes into body water, and lean tissue holds more of it than fat, which is the whole of the sex difference the equation captures
- the ÷ 10
- r × W(kg) is the distribution volume in litres, so A ÷ (r · W) is grams per litre. Grams per 100 mL is one tenth of that, hence the 10. A BAC in g/100 mL is numerically the same as the percentage figure used in law enforcement and as mg/100 mL divided by a thousand
- β
- the elimination rate, in g/100 mL of blood per hour. Ethanol follows zero-order kinetics above about 20 mg/100 mL because alcohol dehydrogenase is saturated, which is why this is a straight subtraction rather than an exponential decay
- what is NOT in the equation
- any absorption term at all. Widmark assumes every gram entered is already in the blood and distributed — so during the absorption phase, which Jones calls the most variable and unpredictable part of ethanol pharmacokinetics, the equation is simply wrong rather than imprecise
Worked example
An 80 kg man, three 568 mL drinks at 4.5% ABV, three hours since the first drink, β 0.015 g/100 mL/h
Ethanol: 3 × 568 mL = 1,704 mL of drink; × 4.5 ÷ 100 = 76.68 mL of ethanol; × 0.789 g/mL = 60.5 g
Distribution volume: 0.68 L/kg × 80 kg = 54.4 L
Peak, before any elimination: 60.5 ÷ (10 × 0.68 × 80) = 0.111 g/100 mL
Elimination over three hours: 0.015 × 3 = 0.045
Point estimate: 0.111 − 0.045 = 0.066 g/100 mL, which is 66 mg/100 mL, or 0.066% BAC
Now the number that matters. Propagating the published standard deviations — r 0.067 L/kg for men, β 0.0032 g/100 mL/h, and 1% on the density constant — gives a combined standard uncertainty of 0.0146, so the two-standard-deviation range is 0.037 to 0.095 g/100 mL
That range straddles both limits. Its lower bound, 37 mg/100 mL, is comfortably under Scotland's 50 mg/100 mL. Its upper bound, 95 mg/100 mL, is over the 80 mg/100 mL that applies in England, Wales and Northern Ireland. The same three pints in the same man, calculated correctly, is consistent with being well under one limit and well over the other
Which is the answer to the only question anybody actually asks this calculator. It cannot tell you whether this man was over a limit, and it cannot tell you whether he was fit to drive. A measured breath or blood sample can. This cannot
What the range is built from
| Parameter | Value used | Published uncertainty | Source |
|---|---|---|---|
| r, men | 0.68 L/kg | SD 0.067 L/kg (CV 9.2%) | Gullberg 2007, from Dubowski’s series of 24 males. Independently corroborated by Jones’s 2019 survey, whose best-performing male equation has a 95% range of ±0.13 L/kg — implying an SD of 0.066 |
| r, women | 0.55 L/kg | SD 0.077 L/kg, derived | Jones 2019 gives the best-performing female equation a range of ±0.15 L/kg. Treated as a 95% range, that implies an SD of 0.15 ÷ 1.96 = 0.0765. No paper publishes a female SD directly, so this one figure on the page is a derivation rather than a quotation, and is labelled as such |
| β | your input, default 0.015 | SD 0.0032 g/100 mL/h (CV 22%) | Gullberg 2007, from Dubowski’s series of 25 males. The JAAPL forensic toxicology review gives a weighted mean and SD of 0.0155 ± 0.0029 for social drinkers and 0.0249 ± 0.0049 for alcoholics — close agreement from a different pooling |
| Ethanol density | 0.789 g/mL | CV 1% | Gullberg 2007 assigns a 1% coefficient of variation to the density constant. It is the smallest of the three contributions by an order of magnitude |
| Body weight, drink volume, ABV, elapsed time | your inputs | not propagated | Gullberg propagates these too and arrives at a 21.2% CV for his example where this method gives 22.1% for its own. The range on this page is therefore if anything narrower than the truth, because it treats four inputs nobody actually knows precisely as though they were exact |
Everything the equation ignores
| Ignored | What actually happens | Effect on the estimate |
|---|---|---|
| The absorption phase | Widmark has no absorption term. It assumes every gram entered is already in the blood and evenly distributed. Jones calls the absorption stage “undoubtedly the most variable and unpredictable aspect of ethanol pharmacokinetics” | Inside the first one to two hours of drinking the estimate is not imprecise, it is inapplicable. It will usually overestimate, because it credits the blood with alcohol still in the stomach |
| Food | A heavy breakfast reduced the area under the blood alcohol curve by 63% in one study; protein, fat and carbohydrate meals reduced absorption by 77%, 90% and 96% respectively | Large and unpredictable overestimation after a meal. The equation has no term for it, and neither does any Widmark calculator |
| Bioavailability | The calculation assumes 100% availability of the oral dose. First-pass metabolism in the stomach and liver removes a variable fraction, and that fraction differs with sex, dose, food and the strength of the drink | Systematic overestimation of an unknown size |
| Sex, beyond r | The r selector captures body composition. It does not capture the elimination slope, which Jones reports is “slightly steeper in women compared with men”, related to liver weight relative to lean body mass | β must be chosen separately, and this page will not choose it for you by sex — the published sex difference in β is small relative to the 22% coefficient of variation around it |
| Tolerance | A heavy drinker may be conversant at a concentration that would render a naive drinker unconscious, and eliminates alcohol faster: 0.025–0.035 g/100 mL/h in alcoholics during detoxification against 0.010–0.020 in social drinkers | The estimate is a concentration and never a measure of impairment. Two people at 0.10 g/100 mL are not equally impaired and not equally safe |
| Whether the drinks were what was said | The drink count, the volume poured and the ABV are all reported by someone, and home measures are notoriously larger than standard ones | Not in the range at all. This is usually the largest error in practice and it is the one no propagation can quantify |
Limits, and which side of them exactly-on-the-limit falls
| Jurisdiction | Blood limit | Statutory wording | Exactly on the limit |
|---|---|---|---|
| England, Wales, Northern Ireland | 80 mg/100 mL | Road Traffic Act 1988 s.5(1) — the proportion must exceed the prescribed limit; s.11(2) sets it at 80 milligrammes in 100 millilitres of blood | Not an offence. 80.0 does not exceed 80 |
| Scotland | 50 mg/100 mL | Same Act, same “exceeds” wording, limit reduced for Scotland in 2014 | Not an offence |
| United States, most states | 0.08 g/dL | Typically framed as at or above 0.08, and 0.04 for commercial drivers | An offence, in the other direction from the UK wording |
| Breath and urine, UK | 35 µg/100 mL breath · 107 mg/100 mL urine | Road Traffic Act 1988 s.11(2) | Same “exceeds” wording throughout |
Why this page refuses to give you one number
Widmark’s equation is a good piece of pharmacokinetics that is almost always used for the wrong purpose. Erik Widmark worked out in the 1920s and 1930s that ethanol distributes into body water, that the distribution volume can be summarised as a factor r of about 0.68 L/kg in men and 0.55 L/kg in women, and that it is eliminated at a nearly constant rate rather than exponentially, because alcohol dehydrogenase saturates after the first drink or two. From those three facts a concentration follows from a dose, a body weight and a time. Gullberg’s published form solves it the other way — for the number of drinks that would explain a measured concentration — which is what it is genuinely for: a forensic expert with an analysed blood sample, a known time of sampling and a disputed drinking history, reasoning backwards in front of a court.
Used forwards, as a calculator that turns drinks into a blood alcohol concentration, it is a different and much weaker thing. It has no absorption term, so it assumes every gram you enter is already in your blood and evenly distributed — which inside the first hour or two of drinking is not an approximation but a false premise. It assumes the whole oral dose reached the circulation, ignoring first-pass metabolism. It has no term for food, and a meal can reduce the area under the blood alcohol curve by more than half. It takes the drink count, the pour size and the strength on trust. And it captures the difference between men and women only through r, not through the elimination slope, which also differs.
None of that is the reason this page carries a range rather than a number. The reason is that even when every input is correct, the two parameters at the heart of the equation vary enormously between people, and both variations have been measured. Gullberg reports a standard deviation of 0.067 L/kg on r in men — a coefficient of variation of 9.2% — and 0.0032 g/100 mL/h on β, a coefficient of variation of 22%. Jones’s evidence-based survey puts the whole physiological span of the elimination rate at 0.010 to 0.035 g/100 mL/h. Propagate those through the equation and the answer comes back with a two-standard-deviation interval of roughly 40% either side, which is very close to the 42% Gullberg recommends be quoted whenever a BAC estimate is reported at all.
What that means in practice is visible in this page’s own default example. An 80 kg man, three pints at 4.5%, three hours: the point estimate is 0.066 g/100 mL, and the plausible range is 0.037 to 0.095. The lower bound is well under the 50 mg/100 mL limit that applies in Scotland. The upper bound is well over the 80 mg/100 mL that applies in England, Wales and Northern Ireland and, as 0.08 g/dL, across most of the United States. Done correctly, with published parameters and published uncertainties, the calculation is consistent with being comfortably legal and comfortably illegal at the same time. It cannot distinguish between those two people, and neither can any other Widmark calculator — the ones that show a single confident figure are hiding this, not avoiding it.
So the only honest use of this page is to understand the shape of the arithmetic, and the only honest conclusion to draw from it is that an estimate cannot answer the question people want answered. A Widmark estimate cannot tell anyone whether they are fit or legal to drive, and must not be used for that. Nothing here substitutes for an analysed breath or blood specimen, and the safe interpretation of any estimate near a limit is that the estimate does not know. For a measured concentration and the units it gets reported in, use the blood alcohol unit converter; for ethanol’s contribution to a raised osmolal gap in a patient being screened for a toxic alcohol, the osmolal gap calculator subtracts it properly.
Frequently asked questions
Can this calculator tell me whether I am safe or legal to drive?
No, and it is important to be blunt about why rather than just disclaiming it. On this page’s own default inputs the plausible range is 0.037 to 0.095 g/100 mL — below Scotland’s 50 mg/100 mL limit at one end and above the 80 mg/100 mL limit at the other. The calculation cannot distinguish between someone comfortably under and someone comfortably over, because the between-person variation in the volume of distribution and in the elimination rate is that large and has been measured to be that large. A Widmark estimate is a retrospective forensic reconstruction used by expert witnesses with a measured concentration and a known drinking history. It is not a prospective tool and it must not be used to decide whether to drive.
Why does the page show a range instead of one number?
Because the published parameters come with published standard deviations, and ignoring them produces false confidence. Gullberg’s 2007 uncertainty analysis of exactly this equation gives r a standard deviation of 0.067 L/kg in men (coefficient of variation 9.2%) and the elimination rate a standard deviation of 0.0032 g/100 mL/h (coefficient of variation 22%), and concludes that a reported BAC estimate should carry an uncertainty interval of approximately 42%. The range here is that propagation, at two standard deviations. It is narrower than Gullberg’s, because he also propagates uncertainty in the body weight, the ethanol per drink and the elapsed time, which this page treats as exact.
What elimination rate should I use?
Jones’s evidence-based survey of blood ethanol elimination rates gives the physiological range as 0.010 to 0.035 g/100 mL/h: 0.010 to 0.015 after drinking on an empty stomach, 0.015 to 0.020 when not fasted, and 0.025 to 0.035 in alcoholics during detoxification, where microsomal CYP2E1 activity is boosted. He suggests 0.015 g/100 mL/h as a good population average and 0.019 for apprehended drivers, because many of those individuals are binge drinkers or alcoholics. The default here is 0.015. Note that the choice moves the estimate by 0.015 g/100 mL for every hour of elapsed time, so over five hours the two ends of the range differ by 0.125 g/100 mL — more than the entire legal limit.
Is the 0.8 in the usual version of the formula really the density of ethanol?
Effectively yes, though the correctly derived constant is 0.823 rather than 0.8. Gullberg publishes it as d = 0.82 oz/fl oz, and ethanol’s density of 0.789 g/mL converts to exactly that: 0.789 × 29.5735 mL per US fluid ounce ÷ 28.3495 g per ounce = 0.8231 oz/fl oz. It only looks like a mystery constant because the traditional form of the equation mixes ounces of ethanol with ounces of body weight. Computing in metric, as this page does, removes it: grams of ethanol divided by ten times the distribution volume in litres gives grams per 100 mL directly.
Why is exactly 80 mg/100 mL treated as below the limit?
Because that is what the statute says. Section 5(1) of the Road Traffic Act 1988 makes it an offence to drive when the proportion of alcohol in breath, blood or urine exceeds the prescribed limit, and section 11(2) sets that limit at 80 milligrammes of alcohol in 100 millilitres of blood. A concentration of exactly 80.0 does not exceed 80, so it falls below the limit. Most United States statutes are framed the other way, as at or above 0.08 g/dL, where exactly 0.08 is an offence. That is a genuine difference in the law and this page’s bands follow the UK wording rather than blurring it.
Does a low estimate mean someone is sober?
No. A concentration is not a measure of impairment, in either direction. Tolerance in a heavy drinker can be extreme, so a high concentration does not always produce the impairment expected of it; and impairment of divided attention and reaction time is measurable at concentrations well below any legal limit in someone without tolerance. In a clinical setting the further point is that ethanol never explains a reduced conscious level by itself until head injury, hypoglycaemia, sepsis, a co-ingestion and a toxic alcohol have been considered — a low ethanol in a drowsy patient is a reason to look harder, not to stop looking.
Related calculators
References
- Gullberg RG. Estimating the uncertainty associated with Widmark’s equation as commonly applied in forensic toxicology. Forensic Sci Int. 2007;172(1):33–39. Publishes N = W·r·[Ct + βt]/(d·Z) with W in ounces, r in L/kg, β in kg/L/h, d = 0.82 oz/fl oz (CV 1%); r 0.73 ± 0.067 L/kg and β 0.000148 ± 0.000032 kg/L/h from Dubowski’s series; recommends a 2CV uncertainty interval of approximately 42% when reporting an estimated BAC and 25% when reporting a number of drinks.
- Jones AW. Evidence-based survey of the elimination rates of ethanol from blood with applications in forensic casework. Forensic Sci Int. 2010;200(1–3):1–20. Fasted 10–15 mg/100 mL/h; non-fasted 15–20; alcoholics during detoxification 25–35; physiological range 10–35 mg/100 mL/h; 15 mg/100 mL/h a good population average and 19 mg/100 mL/h more appropriate for apprehended drivers.
- Jones AW. Evidence based survey of the distribution volume of ethanol: comparison of empirically determined values with anthropometric measures. Forensic Sci Int. 2019. 173 male and 63 female subjects; Widmark’s original factors 0.68 for men and 0.55 for women; the Watson equation best for males (bias 0.00 L/kg, 95% range ±0.13 L/kg) and the Forrest BMI-based equation best for females (bias −0.01 L/kg, range ±0.15 L/kg).
- Ethanol Forensic Toxicology. J Am Acad Psychiatry Law. 2017;45(4):429–438. Blood ethanol disappearance rate weighted mean and standard deviation 0.0155 ± 0.0029 %/h in social drinkers and 0.0249 ± 0.0049 %/h in alcoholics, with a 95% population range of 0.010 to 0.022 %/h; a heavy breakfast reduced the area under the curve by 63%, and protein, fat and carbohydrate meals reduced absorption by 77%, 90% and 96%.
- Dubowski KM. Human pharmacokinetics of ethanol. I. Peak blood concentrations and elimination in male and female subjects. Alcohol Tech Rep. 1976;5:55–63. The source series (24 males for r, 25 for β) from which the standard deviations used on this page derive.
- Road Traffic Act 1988, sections 5 and 11. Section 5(1) makes it an offence to drive when the proportion of alcohol in breath, blood or urine exceeds the prescribed limit; section 11(2) sets the prescribed limit at 35 microgrammes of alcohol in 100 millilitres of breath, 80 milligrammes in 100 millilitres of blood and 107 milligrammes in 100 millilitres of urine. The Scottish blood limit was reduced to 50 milligrammes in 100 millilitres in 2014.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.